材料力學課件第十三章彎曲的幾個補充問題

1、 FyFzFzFj jFyFzyxz撓曲線撓曲線梁的軸線梁的軸線對稱軸對稱軸垂直縱向?qū)ΨQ面垂直縱向?qū)ΨQ面xyz梁的軸線梁的軸線對稱軸對稱軸水平縱向?qū)ΨQ面水平縱向?qū)ΨQ面撓曲線撓曲線FyFzmmzyMyxMz mmzyMyxMzzIMyy yIMzz yIMzIMzzyy C ( y,z ) e ( z0 ,y0 )000 yIMzIMzzyye yIMzIMzzyy zyxzOe (z0,y0)000 yIMzIMzzyy中性軸中性軸000 yIMzIMzzyyj j cottan00 zyzyyzIIIIMMyzzyx 中性軸中性軸z0 22zyMMM yzO M中性軸中性軸 tantan00

2、 zyzyyzIIIIMMyzyzMM tan yx 中性軸中性軸 z yO 討討 論：論：z tantan00zyzyyzIIIIMMyz tantan00zyzyyzIIIIMMyz 中性軸中性軸 z yOM 中性軸D2D1OD1D2zy中性軸中性軸中性軸中性軸D2D1max wzwyw 22zywww yzww tan xA B CzyF2=2kNF1=1kN 0.5m 0.5m 4080zyO xA B CzyF2=2kNF1=1kN 0.5m 0.5m xA B CzyF2=2kNF1=1kN 0.5m 0.5m 1kNmMz(x)圖圖1kNmMy(x)圖圖zyxMyzyxzzyx拉

3、拉拉拉壓壓D2D18040zyyyyWM max zzzWM max 2408061 yW2804061 zW22408061mkN1804061mkN1 yyzzWMWMMPa02. 7)max(1 yyzzDWMWM MPa02. 7)max(2 D zyxMyzyxz拉拉拉拉壓壓41101101128040124080tan3333 yzzyMMII 14 zy中性軸中性軸 8040zy中性軸中性軸 1+-拉拉壓壓40Fqaayzz40FqaayFyFzqaFFqaFFzy321. 040sin383. 040cos FzACBxz面面qFyACBxy面面DD0.617abcda0.45

4、6qa20.266qa20.383qa2Mz圖圖ac0.321qa20.642qa20.444qa2My圖圖3636m105 .31m10237 yzWWqWMWMyyAzzAA3max105 .21)( qWMWMyyDzzDD3max1002.16)( .)(maxmax qWMWMyyAzzAA3 310105 52121kN/m44. 75 .21101603 q AAAq(x)F1F2tyOmtyzdhbh1hbdy1y1dISFzz*S )4(22221SyhdhbdIFz tyOmtyzdhbh1hbdy1y1q(x)mmnnxdxFSMFSM+dMnmmndxxnmnmdxmn

5、Ozydxm2hDCA111dAADmCdxBF*1NF*2NIhMz21 IhMMz2d11 z*AA*IhMAAAF2dd1*1*11N hIMMFz*2N2d A*mnOzydxm2hDCAADmCdxB111dAF*1NF*2NA*FF*2N*1N ADmCdxBF*1NF*2NSdF 1 1xFdd1S 0d*2NS*1N FFF z*IhMF21N hIMMFz*2N2dzIhF2S1 ADmCdxBF*1NF*2NSdF 1 1 11zIhF2S1 mnOzydxm2hDCA 1 1mmb max1zIhF2S1 zIbhF2Smax1 yOmyzdhbh1hbdy1y1)4(22221SyhdhbdIFz 11()2R2ddhhFAdy* *A A)()4(2222221SdyyhdhbIFhhz yOmyzdhbh1hbdy1y1 1